Question

Hello, I need some help with composite functions.

g(x) = x + 5
h(x) = x^2


Find x, if hg(x) = h(x)

Please provide proper steps inside of direct answer, thank you.

Answer 1

I read this as (h of g)(x)=h(x). This is h(g(x))=h(x), h(x+5)=x², (x+5)²=x².
x²+10x+25=x², 10x=-25, x=-2.5.
CHECK: g(-2.5)=2.5; h(2.5)=6.25=(-2.5)²